Square Root Calculator
Square Root Calculator
The square root function finds a number that, when squared, equals the input. It is one of the most fundamental operations in mathematics.
Conversion Formula
√n = n^(1/2). The result is the principal (positive) square root. For perfect squares, the result is an integer.
Step-by-Step Examples
144 = 12
12 × 12 = 144, a perfect square.
2 = 1.4142135624
√2 is irrational, approximately 1.414.
Frequently Asked Questions
What is a square root?
The square root of n is the number that, when multiplied by itself, gives n. √25 = 5 because 5 × 5 = 25.
Can you take the square root of a negative number?
Not in real numbers. The square root of a negative number involves imaginary numbers: √(-1) = i.
What is a perfect square?
A perfect square is a number whose square root is a whole number. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
Is √2 a rational number?
No. √2 ≈ 1.41421356... is irrational — it cannot be expressed as a fraction and its decimal never terminates or repeats.
How was square root calculated before calculators?
Ancient methods included the Babylonian method (repeated averaging), geometric constructions, and Newton's method (iterative approximation).